Neyman-Pearson lemma

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In statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H0: θ=θ0 and H1: θ=θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when

\Lambda(x)=\frac{ L( \theta _{0} \mid x)}{ L (\theta _{1} \mid x)} \leq k \mbox{ where } Pr(\Lambda(X)\leq k|H_0)=\alpha

is the most powerful test of size α.

The lemma is named for Jerzy Neyman and Egon Pearson.

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